{"id":1252,"date":"2019-06-07T13:45:44","date_gmt":"2019-06-07T17:45:44","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/?post_type=back-matter&p=1252"},"modified":"2019-10-09T13:45:49","modified_gmt":"2019-10-09T17:45:49","slug":"answer-key-2-3","status":"publish","type":"back-matter","link":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/back-matter\/answer-key-2-3\/","title":{"raw":"Answer Key 2.3","rendered":"Answer Key 2.3"},"content":{"raw":"[latexpage]\r\n
    \r\n \t
  1. \\(\\begin{array}{rrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n2&-(-3a&-&8)&=&1 \\\\\r\n-2&&&&&-2 \\\\\r\n\\midrule\r\n&-(-3a&-&8)&=&-1 \\\\\r\n&3a&+&8&=&-1 \\\\\r\n&&-&8&&-8 \\\\\r\n\\midrule\r\n&&&3a&=&-9 \\\\\r\n&&&a&=&-3\r\n\\end{array}\\)<\/li>\r\n \t
  2. \\(\\begin{array}{rrcrc}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n2(-3n&+&8)&=&-20\\\\ \\\\\r\n\\dfrac{2}{2}(-3n&+&8)&=&\\dfrac{-20}{2} \\\\ \\\\\r\n-3n&+&8&=&-10 \\\\\r\n&-&8&&-8 \\\\\r\n\\midrule\r\n&&\\dfrac{-3n}{-3}&=&\\dfrac{-18}{-3} \\\\ \\\\\r\n&&n&=&6\r\n\\end{array}\\)<\/li>\r\n \t
  3. \\(\\begin{array}{rrcrc}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n-5(-4&+&2v)&=&-50\\\\ \\\\\r\n\\dfrac{-5}{-5}(-4&+&2v)&=&\\dfrac{-50}{-5}\\\\ \\\\\r\n-4&+&2v&=&10 \\\\\r\n+4&&&&+4 \\\\\r\n\\midrule\r\n&&\\dfrac{2v}{2}&=&\\dfrac{14}{2}\\\\ \\\\\r\n&&v&=&7\r\n\\end{array}\\)<\/li>\r\n \t
  4. \\(\\begin{array}{rrcrrrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n2&-&8(-4&+&3x)&=&34 \\\\\r\n-2&&&&&&-2 \\\\\r\n\\midrule\r\n&&\\dfrac{-8}{-8}(-4&+&3x)&=&\\dfrac{32}{-8} \\\\ \\\\\r\n&&-4&+&3x&=&-4 \\\\\r\n&&+4&&&&+4 \\\\\r\n\\midrule\r\n&&&&3x&=&0 \\\\\r\n&&&&x&=&0\r\n\\end{array}\\)<\/li>\r\n \t
  5. \\(\\begin{array}{rrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n\\dfrac{66}{6}&=&\\dfrac{6}{6}(6&+&5x) \\\\ \\\\\r\n11&=&6&+&5x \\\\\r\n-6&&-6&& \\\\\r\n\\midrule\r\n\\dfrac{5}{5}&=&\\dfrac{5x}{5}&& \\\\ \\\\\r\nx&=&1&&\r\n\\end{array}\\)<\/li>\r\n \t
  6. \\(\\begin{array}{rrcrcrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n32&=&\\phantom{-}2&-&5(-4n&+&6) \\\\\r\n-2&&-2&&&& \\\\\r\n\\midrule\r\n\\dfrac{30}{-5}&=&\\dfrac{-5}{-5}(-4n&+&6)&& \\\\ \\\\\r\n-6&=&-4n&+&6&& \\\\\r\n-6&&&-&6&& \\\\\r\n\\midrule\r\n\\dfrac{-12}{-4}&=&\\dfrac{-4n}{-4}&&&& \\\\ \\\\\r\nn&=&3&&&&\r\n\\end{array}\\)<\/li>\r\n \t
  7. \\(\\begin{array}{rrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n-2&+&2(8x&-&9)&=&-16 \\\\\r\n+2&&&&&&+2 \\\\\r\n\\midrule\r\n&&\\dfrac{2}{2}(8x&-&9)&=&\\dfrac{-14}{2} \\\\ \\\\\r\n&&8x&-&9&=&-7 \\\\\r\n&&&+&9&&+9 \\\\\r\n\\midrule\r\n&&&&8x&=&2 \\\\ \\\\\r\n&&&&x&=&\\dfrac{1}{4}\r\n\\end{array}\\)<\/li>\r\n \t
  8. \\(\\begin{array}{rrrrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\\r\n-3&+&5n&=&12 \\\\\r\n+3&&&&+3 \\\\\r\n\\midrule\r\n&&\\dfrac{5n}{5}&=&\\dfrac{15}{5} \\\\ \\\\\r\n&&n&=&3\r\n\\end{array}\\)<\/li>\r\n \t
  9. \\(\\begin{array}{rrrrlll}\r\n\\\\ \\\\ \\\\\r\n-1&-&7m&=&-8m&+&7 \\\\\r\n-7&+&7m&&+7m&-&7 \\\\\r\n\\midrule\r\n&&(-8&=&-m)(-1)&& \\\\\r\n&&m&=&8&&\r\n\\end{array}\\)<\/li>\r\n \t
  10. \\(\\begin{array}{rrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\\r\n56p&-&48&=&6p&+&2 \\\\\r\n-6p&+&48&&-6p&+&48 \\\\\r\n\\midrule\r\n&&\\dfrac{50p}{50}&=&\\dfrac{50}{50}&& \\\\ \\\\\r\n&&p&=&1&&\r\n\\end{array}\\)<\/li>\r\n \t
  11. \\(\\begin{array}{rrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\\r\n1&-&12r&=&29&-&8r \\\\\r\n-1&+&8r&&-1&+&8r \\\\\r\n\\midrule\r\n&&\\dfrac{-4r}{-4}&=&\\dfrac{28}{-4}&& \\\\ \\\\\r\n&&r&=&-7&&\r\n\\end{array}\\)<\/li>\r\n \t
  12. \\(\\begin{array}{rrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\\r\n4&+&3x&=&-12x&+&4 \\\\\r\n-4&+&12x&&+12x&-&4 \\\\\r\n\\midrule\r\n&&15x&=&0&& \\\\\r\n&&x&=&0&&\r\n\\end{array}\\)<\/li>\r\n \t
  13. \\(\\begin{array}{rrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\\r\n20&-&7b&=&-12b&+&30 \\\\\r\n-20&+&12b&&+12b&-&20 \\\\\r\n\\midrule\r\n&&\\dfrac{5b}{5}&=&\\dfrac{10}{5}&& \\\\ \\\\\r\n&&b&=&2&&\r\n\\end{array}\\)<\/li>\r\n \t
  14. \\(\\begin{array}{rrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\\r\n-16n&+&12&=&39&-&7n \\\\\r\n+7n&-&12&&-12&+&7n \\\\\r\n\\midrule\r\n&&\\dfrac{-9n}{-9}&=&\\dfrac{27}{-9}&& \\\\ \\\\\r\n&&n&=&-3&&\r\n\\end{array}\\)<\/li>\r\n \t
  15. \\(\\begin{array}{rrrrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n-2&-&5(2&-&4m)&=&33&+&5m \\\\\r\n+2&&&&&&+2&& \\\\\r\n\\midrule\r\n&&-10&+&20m&=&35&+&5m \\\\\r\n&&+10&-&5m&&+10&-&5m \\\\\r\n\\midrule\r\n&&&&\\dfrac{15m}{15}&=&\\dfrac{45}{15}&& \\\\ \\\\\r\n&&&&m&=&3&&\r\n\\end{array}\\)<\/li>\r\n \t
  16. \\(\\begin{array}{rrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\\r\n-25&-&7x&=&12x&-&6 \\\\\r\n+25&-&12x&&-12x&+&25 \\\\\r\n\\midrule\r\n&&\\dfrac{-19x}{-19}&=&\\dfrac{19}{-19}&& \\\\ \\\\\r\n&&x&=&-1&&\r\n\\end{array}\\)<\/li>\r\n \t
  17. \\(\\begin{array}{rrrrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n-4n&+&11&=&2&-&16n&+&3n \\\\\r\n+16n&-&11&&-11&+&16n&-&3n \\\\\r\n-3n&&&&&&&& \\\\\r\n\\midrule\r\n&&\\dfrac{9n}{9}&=&\\dfrac{-9}{9}&&&& \\\\ \\\\\r\n&&n&=&-1&&&&\r\n\\end{array}\\)<\/li>\r\n \t
  18. \\(\\begin{array}{rrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\\r\n-7&-&7b&=&-5&-&5b \\\\\r\n+7&+&5b&&+7&+&5b \\\\\r\n\\midrule\r\n&&\\dfrac{-2b}{-2}&=&\\dfrac{2}{-2}&& \\\\ \\\\\r\n&&b&=&-1&&\r\n\\end{array}\\)<\/li>\r\n \t
  19. \\(\\begin{array}{rrrrlrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n-6v&-&29&=&-4v&-&5v&-&5 \\\\\r\n+4v&+&29&&+4v&+&5v&+&29 \\\\\r\n+5v&&&&&&&& \\\\\r\n\\midrule\r\n&&\\dfrac{3v}{3}&=&\\dfrac{24}{3}&&&& \\\\ \\\\\r\n&&v&=&8&&&&\r\n\\end{array}\\)<\/li>\r\n \t
  20. \\(\\begin{array}{rrcrrrr}\r\n\\\\ \\\\ \\\\\r\n-64r&+&16&=&3r&+&16 \\\\\r\n-3r&-&16&&-3r&-&16 \\\\\r\n\\midrule\r\n&&-67r&=&0&& \\\\\r\n&&r&=&0&&\r\n\\end{array}\\)<\/li>\r\n \t
  21. \\(\\begin{array}{rrcrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\\r\n8x&-&8&=&-20&-&4x \\\\\r\n+4x&+&8&&+8&+&4x \\\\\r\n\\midrule\r\n&&\\dfrac{12x}{12}&&\\dfrac{-12}{12}&& \\\\ \\\\\r\n&&x&=&-1&&\r\n\\end{array}\\)<\/li>\r\n \t
  22. \\(\\begin{array}{rrrrlrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n-8n&-&19&=&-16n&+&6&+&3n \\\\\r\n+16n&+&19&&+16n&+&19&-&3n \\\\\r\n-3n&&&&&&&& \\\\\r\n\\midrule\r\n&&\\dfrac{5n}{5}&=&\\dfrac{25}{5}&&&& \\\\ \\\\\r\n&&n&=&5&&&&\r\n\\end{array}\\)<\/li>\r\n \t
  23. \\(\\begin{array}{rrrrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n-2m&+&4&+&7m&-&56&=&-67 \\\\\r\n&-&4&&&+&56&&+56 \\\\\r\n&&&&&&&&-4 \\\\\r\n\\midrule\r\n&&&&&&\\dfrac{5m}{5}&=&\\dfrac{-15}{5} \\\\ \\\\\r\n&&&&&&m&=&-3\r\n\\end{array}\\)<\/li>\r\n \t
  24. \\(\\begin{array}{rrlrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\\r\n7&=&4n&-&28&+&35n&+&35 \\\\\r\n+28&&&+&28&&&-&35 \\\\\r\n-35&&&&&&&& \\\\\r\n\\midrule\r\n0&=&39n&&&&&& \\\\\r\nn&=&0&&&&&&\r\n\\end{array}\\)<\/li>\r\n \t
  25. \\(\\begin{array}{rrlrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\\r\n50&=&\\phantom{-}56&+&56r&-&4r&-&6 \\\\\r\n-56&&-56&&&&&+&6 \\\\\r\n+6&&&&&&&& \\\\\r\n\\midrule\r\n0&=&52r&&&&&& \\\\\r\nr&=&0&&&&&&\r\n\\end{array}\\)<\/li>\r\n \t
  26. \\(\\begin{array}{rrrrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n-48&-&48x&-&12&+&24x&=&-12 \\\\\r\n+48&&&+&12&&&&+12 \\\\\r\n&&&&&&&&+48 \\\\\r\n\\midrule\r\n&&&&&&\\dfrac{-24x}{-24}&=&\\dfrac{48}{-24} \\\\ \\\\\r\n&&&&&&x&=&-2\r\n\\end{array}\\)<\/li>\r\n<\/ol>","rendered":"
      \n
    1. \"\begin{array}{rrrrrr}<\/li>\n
    2. \"\begin{array}{rrcrc}<\/li>\n
    3. \"\begin{array}{rrcrc}<\/li>\n
    4. \"\begin{array}{rrcrrrl}<\/li>\n
    5. \"\begin{array}{rrrrr}<\/li>\n
    6. \"\begin{array}{rrcrcrr}<\/li>\n
    7. \"\begin{array}{rrrrrrr}<\/li>\n
    8. \"\begin{array}{rrrrl}<\/li>\n
    9. \"\begin{array}{rrrrlll}<\/li>\n
    10. \"\begin{array}{rrrrrrr}<\/li>\n
    11. \"\begin{array}{rrrrrrr}<\/li>\n
    12. \"\begin{array}{rrrrrrr}<\/li>\n
    13. \"\begin{array}{rrrrrrr}<\/li>\n
    14. \"\begin{array}{rrrrrrr}<\/li>\n
    15. \"\begin{array}{rrrrrrrrr}<\/li>\n
    16. \"\begin{array}{rrrrrrr}<\/li>\n
    17. \"\begin{array}{rrrrrrrrr}<\/li>\n
    18. \"\begin{array}{rrrrrrr}<\/li>\n
    19. \"\begin{array}{rrrrlrrrr}<\/li>\n
    20. \"\begin{array}{rrcrrrr}<\/li>\n
    21. \"\begin{array}{rrcrrrr}<\/li>\n
    22. \"\begin{array}{rrrrlrrrr}<\/li>\n
    23. \"\begin{array}{rrrrrrrrr}<\/li>\n
    24. \"\begin{array}{rrlrrrrrr}<\/li>\n
    25. \"\begin{array}{rrlrrrrrr}<\/li>\n
    26. \"\begin{array}{rrrrrrrrr}<\/li>\n<\/ol>\n","protected":false},"author":14,"menu_order":12,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"back-matter-type":[],"contributor":[],"license":[],"class_list":["post-1252","back-matter","type-back-matter","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/1252","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/types\/back-matter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/users\/14"}],"version-history":[{"count":25,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/1252\/revisions"}],"predecessor-version":[{"id":2397,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/1252\/revisions\/2397"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/1252\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/media?parent=1252"}],"wp:term":[{"taxonomy":"back-matter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter-type?post=1252"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/contributor?post=1252"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/license?post=1252"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}